An improved stability criterion for discrete-time time-delayed Lur’e systemwith sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur\u27e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach

Robustness analysis of linear time-varying systems with application to aerospace systems

In recent years significant effort was put into developing analytical worst-case analysis tools to supplement the Verification \& Validation (V\&V) process of complex industrial applications under perturbation. Progress has been made for parameter varying systems via a systematic extension of the bounded real lemma (BRL) for nominal linear parameter varying (LPV) systems to IQCs. However, finite horizon linear time-varying (LTV) systems gathered little attention. This is surprising given the number of nonlinear engineering problems whose linearized dynamics are time-varying along predefined finite trajectories. This applies to everything from space launchers to paper processing machines, whose inertia changes rapidly as the material is unwound. Fast and reliable analytical tools should greatly benefit the V\&V processes for these applications, which currently rely heavily on computationally expensive simulation-based analysis methods of full nonlinear models. The approach taken in this thesis is to compute the worst-case gain of the interconnection of a finite time horizon LTV system and perturbations. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQC). A condition for the worst-case gain of such an interconnection can be formulated using dissipation theory. This utilizes a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst-case gain over a set of admissible IQC multipliers. This problem can then be efficiently solved using custom-tailored meta-heuristic (MH) algorithms. One of the developed algorithms is initially benchmarked against non-tailored algorithms, demonstrating its improved performance. A second algorithm's potential application in large industrial problems is shown using the example of a touchdown constraints analysis for an autolanded aircraft as was as an aerodynamic loads analysis for space launcher under perturbation and atmospheric disturbance. By comparing the worst-case LTV analysis results with the results of corresponding nonlinear Monte Carlo simulations, the feasibility of the approach to provide necessary upper bounds is demonstrated. This comparison also highlights the improved computational speed of the proposed LTV approach compared to simulation-based nonlinear analyses

Robustness analysis of linear time-varying systems with application to aerospace systems

In recent years significant effort was put into developing analytical worst-case analysis tools to supplement the Verification \& Validation (V\&V) process of complex industrial applications under perturbation. Progress has been made for parameter varying systems via a systematic extension of the bounded real lemma (BRL) for nominal linear parameter varying (LPV) systems to IQCs. However, finite horizon linear time-varying (LTV) systems gathered little attention. This is surprising given the number of nonlinear engineering problems whose linearized dynamics are time-varying along predefined finite trajectories. This applies to everything from space launchers to paper processing machines, whose inertia changes rapidly as the material is unwound. Fast and reliable analytical tools should greatly benefit the V\&V processes for these applications, which currently rely heavily on computationally expensive simulation-based analysis methods of full nonlinear models. The approach taken in this thesis is to compute the worst-case gain of the interconnection of a finite time horizon LTV system and perturbations. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQC). A condition for the worst-case gain of such an interconnection can be formulated using dissipation theory. This utilizes a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst-case gain over a set of admissible IQC multipliers. This problem can then be efficiently solved using custom-tailored meta-heuristic (MH) algorithms. One of the developed algorithms is initially benchmarked against non-tailored algorithms, demonstrating its improved performance. A second algorithm's potential application in large industrial problems is shown using the example of a touchdown constraints analysis for an autolanded aircraft as was as an aerodynamic loads analysis for space launcher under perturbation and atmospheric disturbance. By comparing the worst-case LTV analysis results with the results of corresponding nonlinear Monte Carlo simulations, the feasibility of the approach to provide necessary upper bounds is demonstrated. This comparison also highlights the improved computational speed of the proposed LTV approach compared to simulation-based nonlinear analyses

Dynamical Systems; Proceedings of an IIASA Workshop, Sopron, Hungary, September 9-13, 1985

The investigation of special topics in systems dynamics -- uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory -- has become a major issue at the System and Decision Sciences Research Program of IIASA. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under variations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of nonlinear dynamic systems theory to biomathematics and ecology. The proceedings of a workshop on the "Mathematics of Dynamic Processes", dealing with these topics is presented in this volume

Technology for large space systems: A bibliography with indexes (supplement 19)

This bibliography lists 526 reports, articles, and other documents introduced into the NASA scientific and technical information system between January 1, 1988 and June 30, 1988. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Aeronautical engineering, a continuing bibliography with indexes

This bibliography lists 823 reports, articles, and other documents introduced into the NASA scientific and technical information system in November 1984

Business Cycles in Economics

The business cycles are generated by the oscillating macro-/micro-/nano- economic output variables in the economy of the scale and the scope in the amplitude/frequency/phase/time domains in the economics. The accurate forward looking assumptions on the business cycles oscillation dynamics can optimize the financial capital investing and/or borrowing by the economic agents in the capital markets. The book's main objective is to study the business cycles in the economy of the scale and the scope, formulating the Ledenyov unified business cycles theory in the Ledenyov classic and quantum econodynamics